Height vs Weight - Erroneous Data: You will need to use software to answer these

Question

Height vs Weight - Erroneous Data: You will need to use software to answer these questions.

Below is the scatterplot, regression line, and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.

You should be able copy and paste the data by highlighting the entire table.

Answer the following questions regarding the relationship.

(a) Using all 11 data pairs for height and weight, calculate the correlation coefficient. Round your answer to 3 decimal places.
r =  

(b) Is there a significant linear correlation between these 11 data pairs?

Yes

No    

(c) Using only the first 10 data pairs for height and weight, calculate the correlation coefficient. Round your answer to 3 decimal places.
r =  

(d) Is there a significant linear correlation between these 10 data pairs?

Yes

No    

(e) Which statement explains this situation?

The height for the last data pair must be an error.

The erroneous value from the last data pair ruined a perfectly good correlation.    

Despite the low correlation coefficient from part (a), there is probably a significant correlation between height and weight.

All of these are valid statements.

          index height (x) weight (y) inches pounds 1 60 120 2 72 200 3 64 130 4 71 205 5 69 180 6 68 180 7 69 193 8 69 195 9 63 115 10 62 140 11 5.5 160 250 200 o 50 100 50 Height-vs- Weight 20 40 60 Height in Inches 80

Explanation / Answer

a) The statistical software output for correlation is:

Correlation between height (x) and weight (y) is:
0.24638704

Hence,

Correlation coefficient = 0.246

b) No, there is no significant relationship between these 11 data pairs.

c) The statistical software output for correlation is:

Correlation between height (x) and weight (y) is:
0.94727768

Hence,

Correlation coefficient = 0.947

d) Yes, there is a significant linear correlation between these 10 data pairs.

e) Option D is correct. All of these are valid statements.

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